Semantic schema modeling for genetic programming using clustering of building blocks

Semantic schema theory is a theoretical model used to describe the behavior of evolutionary algorithms. It partitions the search space to schemata, defined in semantic level, and studies their distribution during the evolution. Semantic schema theory has definite advantages over popular syntactic schema theories, for which the reliability and usefulness are criticized. Integrating semantic awareness in genetic programming (GP) in recent years sheds new light also on schema theory investigations. This paper extends the recent work in semantic schema theory of GP by utilizing information based clustering. To this end, we first define the notion of semantics for a tree based on the mutual information between its output vector and the target and introduce semantic building blocks to facilitate the modeling of semantic schema. Then, we propose information based clustering to cluster the building blocks. Trees are then represented in terms of the active occurrence of building block clusters and schema instances are characterized by an instantiation function over this representation. Finally, the expected number of schema samples is predicted by the suggested theory. In order to evaluate the suggested schema, several experiments were conducted and the generalization, diversity preserving capability and efficiency of the schema were investigated. The results are encouraging and remarkably promising compared with the existing semantic schema.